Common oscillators for electronics include voltage controlled oscillators, phase shift oscillators and ring oscillators. The voltage controlled oscillators and phase shift oscillators provide sine wave outputs.
FIG. 1 illustrates a voltage controlled oscillator 100, which is capable of providing a sine wave output. Voltage controlled oscillators use tuned or resonant LC circuits 101 (circuits with an inductor L and capacitor C) to establish the oscillation frequency. The illustrated CMOS (Complementary Metal Oxide Semiconductor) voltage controlled oscillator 100 has a resonant circuit 101 that includes two inductors and two capacitors. The two cross-coupled transistors 102A and 102B provide the power gain required to compensate for losses and provide a large output waveform. However, the fabrication of inductors in CMOS integrated circuits is problematic, as the inductors occupy large areas and have low quality (Q) factors due to losses in the silicon substrate. Thus, proposals to eliminate inductor(s) include a proposal to use an active circuit to emulate an inductor and to construct an inductorless circuit with a sharp frequency response, and a proposal to replace the inductor and capacitor with a transmission line. Voltage controlled oscillators are commonly used in radio frequency CMOS integrated circuits in cellular phones and other applications.
FIG. 2 illustrates a phase shift oscillator, which also is capable of producing a sine wave output. Phase shift oscillators have been used in electronic instruments due to their simplicity, and recently have been proposed for use in CMOS circuits. The illustrated phase shift oscillator 200 uses an RC network 201 (circuit network with resistors R and capacitors C) to provide a 180° phase shift at the oscillation frequency to the input of the inverter 203, as well as a desired gain. The resistor and capacitor labels R and C are not intended to imply particular values for the resistors and capacitors or that all of these resistors have the same value and all of these capacitors have the same value.
FIG. 3 illustrates ring oscillator 300. Clock generators in digital circuits commonly use ring oscillators with large and nearly square wave outputs. The illustrated ring oscillator includes a network 301 with an odd number of inverters 303 connected in series. At least three inverters are used to insure a full voltage swing. The oscillation frequency is determined by the propagation or signal delay of the inverters. The frequency of oscillation is lowered by using additional inverters. For a given number of inverter stages (N) and inverter propagation delay (TPROP) for each inverter stage 303, the oscillation frequency (f), which includes both a falling and rising edge, can be represented by the equation:
                    f        =                              1                          2              ⁢                              NT                PROP                                              .                                    (        1        )            
The inverters 203 and 303 illustrated in FIGS. 2 and 3 are CMOS inverters, such as illustrated at 403 in FIG. 4, for example.